Fit a periodically integrated periodic autoregressive model.
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wts |
a univariate time series object. |
detcomp |
a vector indicating the deterministic components included in the auxiliar regression. See
the corresponding item in |
p |
the order of the PAR model. In this version first and second order are considered. |
initvalues |
by default, initial values are computed for the non-linear modeal. However, in this version there may be cases in which the estimates do not converge, giving an error message. In this case, a numeric vector with initial values guessed by the user can be included. |
The following equation is estimated by non-linear least squares
y_t = α_s y_{t-1} + β_s (y_{t-1} - α_{s-1} y_{t-2}) + ε_t,
under the restriction Π_{i=1}^{S} α_i = 1 for s=1,...,S, where S denotes
the number of seasons. Regressors defined in detcomp
can also be included. Obviously, for a first
order PIAR process β parameters are equal to zero.
An object of class fit.piartsm-class
containing the estimated coefficients in the restricted
non-linear model, the residuals, and the periodic autoregressive coefficients. On the basis of the
estimated alpha parameters, the periodically differenced data are also computed. See
fit.piartsm-class
for methods that display this information.
Javier Lopez-de-Lacalle javlacalle@yahoo.es.
P.H. Franses: Periodicity and Stochastic Trends in Economic Time Series (Oxford University Press, 1996).
nls
, fit.ar.par
, and fit.piartsm-class
.
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Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
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